The geometric pre-Calabi–Yau conjecture for Chekanov–Eliashberg dg-algebras

Let $W$ be a stopped Weinstein manifold and let $\Lambda$ be a singular Legendrian submanifold in its boundary. Its Chekanov–Eliashberg dg-algebra is the dg-algebra associated to $\Lambda$ by Legendrian contact homology. Geometric pre-Calabi–Yau conjecture. The Chekanov–Eliashberg dg-algebra of $\Lambda$ admits a geometrically defined pre-Calabi–Yau structure. This conjecture predicts a geometric enhancement of the algebraic structure appearing in the study of singular Legendrians and partially wrapped Fukaya categories; the source does not state a resolution.